Cremona's table of elliptic curves

1547 = 7 · 13 · 17

Field	Data	Notes
Atkin-Lehner	7+ 13- 17-	Signs for the Atkin-Lehner involutions
Class	1547a	Isogeny class
Conductor	1547	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	140777 = 72 · 132 · 17	Discriminant
Eigenvalues	-1 -2  0 7+ -4 13- 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-13,0]	[a1,a2,a3,a4,a6]
Generators	[-1:4:1]	Generators of the group modulo torsion
j	244140625/140777	j-invariant
L	1.1919411510581	L(r)(E,1)/r!
Ω	2.7832139023311	Real period
R	0.42826070610662	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	24752be1 99008g1 13923e1 38675i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1547a1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-1	-2	0	+	-4	-	-	4	6	-2	4	0	0	-4	8	10	-4	-6	-4	8	8	10	-12	-14	-12

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Quadratic twists for elliptic curve 1547a1

-4	8	-3	5	-7	13	17
24752be1	99008g1	13923e1	38675i1	10829a1	20111b1	26299h1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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